KPCAL1-SLSSVM-based Isa furnace fault monitoring method

Abstract

The invention provides an Isa furnace fault monitoring method based on KPCAL1-SLSSVM, and relates to the technical field of fault monitoring in the smelting process of an Isa furnace, and the method comprises the steps: collecting data in the smelting process of the Isa furnace; preprocessing the collected data in the smelting process of the Isa furnace through a feature sample extraction kernel principal component analysis model; t2 statistics and SPE statistics are used as evaluation methods for nonlinear fault diagnosis, and an evaluation index is the degree of extracting a kernel principal component analysis model from a calculated data deviation feature sample; establishing a sparse least square support vector diagnosis model, inputting the recognized fault into the model for analysis, and completing the recognition and classification of the fault; and finally verifying the model. According to the method, the feature samples are extracted through fuzzy mean clustering, so that the dimensionality and the calculation amount of a kernel matrix are effectively reduced; and in combination with sparse processing, the number of support vectors is reduced, and the real-time performance and generalization ability of the monitoring model are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent control in the Isa furnace smelting process, and specifically relates to a fault monitoring method for Isa furnace based on KPCAL1-SLSSVM. Background Art

[0002] The Isa furnace is an advanced top-blown bath smelting equipment, which is widely used in the copper smelting field due to its advantages such as compact structure, high smelting efficiency, and good environmental performance. However, its complex high-temperature and multiphase reaction process makes the Isa furnace face monitoring and fault prediction problems brought by characteristics such as multi-variables, non-linearity, and strong coupling during operation. Existing monitoring technologies are mainly based on kernel principal component analysis (KPCA) and least squares support vector machine (LSSVM).

[0003] Although they perform well in non-linear feature extraction and fault classification, they still face key problems in practical applications. KPCA has a high computational complexity when dealing with large data samples, and the curse of dimensionality of the kernel matrix limits its real-time performance; LSSVM needs to process all samples, resulting in too long training time and insufficient real-time performance and adaptability. In addition, the fault characteristics of the Isa furnace are complex, such as problems like lance wear and furnace lining erosion, and there are significant redundancies and noise interferences between related variables, which further reduces the accuracy of fault monitoring. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides a fault monitoring method for Isa furnace based on KPCAL1-SLSSVM.

[0005] To implement the above technical solution, the specific steps are as follows:

[0006] S1. Collect data during the Isa furnace smelting process;

[0007] The collected data includes: temperature data, pressure data, gas and fluid data, furnace lining erosion data, liquid and slag data;

[0008] The correction of the data includes: baseline correction and dynamic correction;

[0009] The rejection methods of the data include: threshold rejection, statistical rejection, and physical constraint rejection; threshold rejection means rejecting when the value of the sampling point is greater than the threshold; when using statistical rejection, the standard deviation rule is used to reject data points exceeding 3 times the standard deviation; when using physical constraint rejection, it is combined with the physical laws of the smelting process for rejection;

[0010] The monitoring of the data is the self-check of the sensor, detecting whether there are breakpoints or a constant value in the output signal of the sensor;

[0011] The judgment of whether the sensor is normal includes: process specifications and historical data;

[0012] S2. Preprocess the data collected during the Isa furnace smelting process through the kernel principal component analysis model (KPCA-L1) for feature sample extraction. The steps are as follows:

[0013] S2.1. Construct the kernel principal component analysis model (KPCA-L1) to reduce the dimension of the data;

[0014] Specifically as follows:

[0015] For the sample set X = {x k | k = 1, 2,..., M} in the input space, where x k ∈R N , where M represents the number of samples and N represents the original dimension of the sample feature space; the original space R maps x k to the high-dimensional space F through the non-linear mapping φ, and the corresponding mapping is φ(x i ) ∈ F. In the high-dimensional space F, the image of the original data x i in the mapping space F is: Assume that the mapped data has zero mean Then the covariance matrix of the mapping function φ(x i ) can be expressed as Equation (1):

[0016]

[0017] To achieve sparse feature selection, an L1 regularization constraint is introduced on the basis of KPCA, and the optimization objective function is:

[0018] min||w|| 1 , subject to w T Cw = λw T w;

[0019] In the formula, w represents the principal component weight vector that meets the sparsity requirement; λ represents the eigenvalue; C represents the covariance matrix in the high-dimensional mapping space, which is used to describe the distribution characteristics of the input samples in the high-dimensional space. Its core role is to provide the covariance information of the principal components for the dimension reduction step and determine the direction of feature projection. The mapping function φ(x i ) maps the input samples from the original space to the high-dimensional space F, and C describes the distribution of all samples φ(x i ) in the high-dimensional space and calculates the covariance relationship between samples;

[0020] In traditional PCA, the eigenvalue λ, λ ≥ 0, and the eigenvector V ∈ F in the equation λV = CV are solved, and then there is Equation (2):

[0021]

[0022] For λ≠0, all eigenvectors v are obtained according to Mercer kernel theory and can be defined as shown in Equation (3):

[0023]

[0024] where α i is the weight coefficient of the mapping function φ(x i ) of the first sample data point x i after mapping. The weight coefficient is automatically generated through an optimization problem. Thus, Equation (2) is expressed as Equation (4);

[0025]

[0026] where m represents the number of effective samples sparsely selected from the high-dimensional feature space; the number of features automatically selected through the L1 regularization in the optimization process satisfies m ≤ M, where M is the number of samples. m is used for normalizing weight calculation, that is, adjusting the elements in the covariance matrix with the number of features after sparse selection, which appears in the weight normalization factor and is used to reduce the influence of unimportant features on the projection direction; x i is the first sample data point after mapping; x j is the second sample data point after mapping, x i， x j ∈R N , x i ≠x j ;

[0027] Define the kernel matrix K as an M×M kernel function matrix, and the elements in the matrix are expressed as:

[0028] k ij =φ(x i )·φ(x j ) (5)

[0029] Therefore, K can be used to simplify Equation (4) to obtain MλKa = K 2 a, that is:

[0030] Mλa = Ka (6)

[0031] where a = [a 1 , a 2 , ···, a m T . By solving Equation (6), the eigenvalue λ and the kernel matrix eigenweight a can be obtained; arrange the eigenvalues of K in descending order λ 1 ≥λ 2 ≥···λ m , and the eigenvectors of K are arranged as v1, v2,..., v m ; ​

[0032] For the eigenvector v of the prediction sample in the high-dimensional F space k The projection onto is given by Equation (7):

[0033]

[0034] Where φ(x) represents the mapped data; Represents the eigenvector projection of x i ;

[0035] When It needs to be adjusted to Equation (8):

[0036]

[0037] Then the elements in the kernel matrix are solved using Equation (9):

[0038]

[0039] Where k ij Represents the elements in the kernel matrix; k im Represents the effective number of elements in the kernel matrix; k nj Represents the index range of the elements in the kernel matrix; k nm Represents the index range of the effective number of the kernel matrix; n represents the index range;

[0040] Based on the above principle, the processing procedure of KPCA-L1 is as follows:

[0041] Represent the sample set X as the input matrix A;

[0042]

[0043] From Equation (5), calculate the kernel matrix K; to eliminate the influence of the sample mean, correct the kernel matrix through the centering method Equation (9) to obtain

[0044] Use the Jacobi iterative method to calculate The eigenvalues λ' 1 ,...,λ' n , that is The eigenvectors v' 1 ,...,v' n ;

[0045] Sort the eigenvalues in descending order (by selection sort) to get λ 1 ′>...>λ n ′ and make corresponding adjustments to the eigenvectors to get v 1 ′,...,v′ n; During the feature extraction process, to achieve sparse dimensionality reduction, the principal component weight vector w that meets the sparsity requirement is added with an L1 regularization constraint;

[0046] Through the projection of the kernel matrix on the extracted feature vectors where a represents the kernel matrix feature weight, a = (a 1 ,..., a t ), t represents the number of features after dimensionality reduction, t ≤ N, and the obtained projection Y is the data obtained after the sample is dimensionally reduced by KPCA;

[0047] S2.2. Construct the kernel principal component analysis method based on feature sample extraction (SKPCA-L1) to improve the model performance;

[0048] Based on PCA, KPCA adds a process of feature sample selection, uses a sparse optimization method to dynamically select feature samples, and improves the performance of PCA;

[0049] KPCA expression: k ij = φ(x i )·φ(x j );

[0050] The dimensionality reduction process depends on eigenvalue decomposition: z i = w T φ(x i );

[0051] The KPCA expression dynamically selects feature samples before calculating K: k ij = φ(x i ) t φ(x j ) dynamically selects x i , optimizing dimensionality reduction;

[0052] The performance improvement includes: computational efficiency, sparsity, real-time performance, and dimensionality reduction effect;

[0053] Computational efficiency: KPCA dynamically selects feature samples during the dimensionality reduction process, reduces the dimension of the kernel matrix, and reduces the computational complexity;

[0054] Sparsity: L1 regularization makes the dimensionality reduction result sparse and improves the interpretability;

[0055] Real-time performance: Sample selection and sparse optimization are suitable for online learning scenarios and improve the real-time performance of the algorithm;

[0056] Dimensionality reduction effect: KPCA is more flexible than PCA in sample feature extraction, can select representative samples, and enhances the effectiveness of the dimensionality reduction result;

[0057] The construction steps are as follows:

[0058] S2.2.1. Feature sample extraction;

[0059] In the feature extraction process of KPCA-L1, the sparse selection of feature samples is achieved through L1 regularization, making the dimensionality reduction result have stronger sparsity and interpretability; the extraction of feature samples is based on the optimization process of sparse weights, as follows:

[0060] Principle of feature sample extraction: The original sample dataset is mapped to the high-dimensional feature space F through φ(x i ), and the data after mapping is φ(x i ); in the high-dimensional feature space F, L sparse feature samples are selected from X to form the feature sample set X i = {x s ,..., x s1} feature sample set S, so that it can represent the entire data distribution; construct the KPCA expression to dynamically select feature samples before calculating K, and its elements are: k sL = φ(x ij ) i )φ(x t ), which captures the non-linear relationship between samples; each mapped sample φ(x j ) can be approximately represented by the weighted sum of feature samples: i where a i = (a i1 ,... a iL ), t , represents the estimated value projected in the optimization direction, and a i is the coefficient vector that minimizes the reconstruction error between and φ i ; the reconstruction error between and φ i can be expressed as: The smaller the reconstruction error, the higher the approximation degree of the feature samples to the original data; in order to achieve the selection of feature samples and ensure sparsity, L1 regularization constraint is introduced, and the optimization objective is: L1 regularization acts on a i , making most of the weights tend to 0 and only retaining a small number of non-zero weights, thus automatically selecting important feature samples;

[0061] The goal of feature sample extraction is to extract the feature sample set S from the sample set, and S satisfies the representativeness index. The representativeness index J s is defined to measure the quality of the feature sample set S;

[0062] Based on the selected feature sample set S, the low-dimensional projection of each sample is represented as eigenvalue decomposition: z i ​= w T φ(x i );

[0063] Covariance matrix optimization: Based on KPCA, the kernel matrix K is optimized by introducing sparse regularization constraints. The final optimization objective is: min||w|| 1 , subject to: w T Cw = λw T w. By optimizing w, the main direction of the feature samples can be obtained, and dimensionality reduction can be achieved;

[0064] Define where J s The value range of is (0,1]. The smaller the value, the stronger the approximation ability of the feature sample set S to the original data;

[0065] The optimization objective is transformed into: That is, given the feature sample L, select the feature sample set that can maximize the representativeness index;

[0066] In the initial state, the feature sample set S is an empty set, and samples are gradually added to it; in each iteration, calculate the reconstruction error δ i and the representativeness index J s , select the sample x that can minimize J s and add it to the feature sample set S, updating the feature sample set S and the reconstruction error; Termination condition: When the size of the feature sample set reaches the preset L, or the reconstruction error δ s converges, stop the iteration; i

[0067] S2.2.2. Perform kernel principal component analysis on the feature samples;

[0068] S2.3. Perform kernel function mapping and sparse feature dimensionality reduction algorithm on the feature samples;

[0069] The traditional PCA algorithm improves the computational efficiency. However, in the process of using PCA for modeling, there are still deficiencies in the selection of initial samples, and the construction from the global distribution of samples is not considered. Therefore, aiming at the characteristics of the data sample distribution of the Isa furnace, this paper proposes a sparse optimization method based on kernel function mapping and L1 regularization. KPCA-L1 is a dimensionality reduction method based on kernel principal component analysis (KPCA) and L1 regularization, aiming to optimize the feature vector weights by introducing L1 regularization to further enhance the sparsity and interpretability of the principal components; The goal of KPCA-L1 is to retain the main linear characteristics of the feature space while achieving effective dimensionality reduction processing;

[0070] Input data set Given the original sample set X = {x k|k = 1, 2, ..., M}, in order to capture the non - linear relationship between samples, the kernel function is used to map the samples from the original space to the high - dimensional feature space F; its mapping form is: φ(x i ) = [φ 1 (x i ), φ 2 (x i ), ..., φ k (x i )] T ; the kernel function k(x i , x j ) is defined as: k(x i , x j ) = φ(x i ) · φ(x j );

[0071] To ensure the centering of K, the kernel matrix is adjusted using Equation (9), and the objective is optimized by the L1 regularization method;

[0072] Eigenvalue decomposition: The adjusted kernel matrix is subjected to eigenvalue decomposition to obtain the eigenvalues λ' and the corresponding eigenvectors v'; the first p eigenvectors with the largest eigenvalues are selected as the principal component directions after dimensionality reduction;

[0073] Dimensionality reduction projection: For each sample x i , its dimensionality reduction result is: z i = w T φ(x i ); the output result of KPCA - L1 is the projection matrix after dimensionality reduction;

[0074] S3. Use the T 2 statistic and the SPE statistic as evaluation methods for non - linear fault diagnosis. The evaluation index is to calculate the degree to which the data deviates from the KPCA - L1 model, and then determine whether a fault has occurred;

[0075] The calculation of the data deviation is automatically calculated through computer simulation;

[0076] The steps are as follows:

[0077] S3.1. Construct the expression of the T 2 statistic;

[0078]

[0079] In the formula: Λ -1 is a diagonal matrix, representing the inverse of the diagonal matrix composed of the eigenvalues corresponding to the first p' principal components;

[0080] T 2The confidence bound expression of the statistic satisfies the F-distribution of Equation (12);

[0081]

[0082] Where: N' represents the number of samples in set S, P′ represents the number of principal components; α represents the projection;

[0083] S3.2. Construct the expression of the squared prediction error (SPE):

[0084]

[0085] Where: when j = k when j ≠ k The confidence bound of the SPE statistic satisfies an approximate distribution of, where g represents the weight parameter of the SPE importance, h is the degree of freedom of the distribution, represents the chi-square distribution with degree of freedom h, t j represents the mapping function from x j to the KPCA-L1 space, the t-th eigenvector of x k ; the t-th eigenvector of x j ;

[0086] S3.3. Analyze through simulation;

[0087] S4. Establish a sparse least squares support vector diagnostic model (SLSSVM), and input the faults identified in S3 into the sparse least squares support vector diagnostic model for analysis to complete the identification and classification of faults; specifically as follows:

[0088] S4.1. Establish a sparse least squares support vector diagnostic model (SLSSVM);

[0089] The support vector machine is a typical representative of statistical machine learning theory and has good generalization ability. In the metallurgical industrial process, it is widely applied to various fault monitoring environments. However, SVM needs to solve the quadratic programming problem under inequality constraint conditions, which increases the difficulty and complexity of the solution. To solve this problem, LSSVM converts the inequality constraint conditions in SVM into equality constraint conditions for solution, reducing the computational complexity. But at the same time, it also brings new problems, that is, LSSVM requires all samples to participate in training, losing the advantage that SVM only needs a limited number of samples to participate in training. For the real-time characteristics of the Isa furnace fault monitoring, LSSVM will inevitably lead to a reduction in timeliness. Therefore, the present invention simplifies LSSVM using the sparse LSSVM algorithm (SLSSVM) and proposes a sparse least squares support vector diagnostic model for Isa furnace fault identification.

[0090] The least squares support vector machine is a model based on the theory of structural risk minimization. Let X' = [x' 1 ,..., x' N' represent the training samples, which in the Isa furnace represent a set composed of N' data samplings, where each sampling contains the data collected during the Isa furnace smelting process; Y' = [y' 1 ,..., y' N' represents the condition of the Isa furnace for each sampling. The formal description of LSSVM is as shown in Equation (14):

[0091]

[0092] In the formula: w′ is the normal vector of the (LSSVM) classification model, b represents the offset, and e k' is the slack variable; γ represents the balance sparsity between the structural risk and the empirical risk; x k' represents the number of principal component mappings;

[0093] Using the Lagrange multiplier method to solve Equation (14), the Lagrangian function can be obtained as follows:

[0094]

[0095] In the formula, L(w', b, e k' , α k' ) is the Lagrangian function; α k' is the Lagrange multiplier; then, taking the derivatives of the variables in Equation (15) respectively, we can get:

[0096]

[0097] Let Y' = [y' 1 ,..., y' N' , 1 v' = [1,..., 1] represents a vector composed of v' 1s; α represents the vector composed of Lagrange multipliers, α = [α 1 ,..., α N' ; Combining the KKT conditions of the optimization theory, Equation (16) can be expressed in matrix form:

[0098]

[0099] In the formula: E represents the identity matrix, Ω = Z T Z, represents the matrix of kernel function values with class information. The elements in Ω are defined as:

[0100]

[0101] where K(xi , x j ) is a kernel function. In kernel methods, the commonly used kernel functions have the following forms:

[0102] Gaussian kernel function, polynomial kernel function, wavelet kernel function, and perceptron kernel function:

[0103] Equation (17) can be used to solve for α k' and b, thereby constructing the final diagnostic function y(x), as shown in Equation (19):

[0104]

[0105] In the equation, y(x) represents the classification output of the model for the input x, and the classification result is +1 or -1; sign represents the sign function, which returns the sign of the input value; α k' represents the Lagrange multiplier, which is obtained through optimization and indicates the weight of the sample; y k' represents the label of the k-th sample, taking values of +1 or -1; K(x, x k ) is the kernel function, indicating the similarity between X and the k-th sample x k ; b represents the bias parameter, which is solved through the optimization problem;

[0106] It can be seen from Equations (17) and (8) that LSSVM requires all sampled data to participate in the training during the training process. It can be seen from Equation (15) that w′ is a linear combination of the input vectors in the feature space. If the maximum linearly independent group of the input vectors in the feature space can be obtained, then an LSSVM with only part of the sampled data participating in the training can be obtained, that is, the sparse LSSVM (SLSSVM). In the specific sparsification process, the method used in the present invention is as follows. The specific SLSSVM model is expressed as:

[0107]

[0108] In the equation: X l is the set of samples with the maximum independence; θ = [θ 1 , θ 1 ,..., θ 1 T ; l is the number of elements in X l ; J p′ (θ) represents the loss function, and the goal is to minimize this function to optimize the model; θ represents the weight vector, which is used to represent the direction of the classification hyperplane in the feature space; similar to solving LSSVM, according to the Lagrange multiplier method, Equation (20) is solved, and the resulting partial derivative equations are converted into an equivalent matrix expression, and then Equation (21) is obtained;

[0109] ​

[0110] In summary, the solution of the SLSSVM is completed.

[0111] S4.2. Construct an Isa furnace diagnosis model based on SLSSVM; the steps are as follows:

[0112] S4.2.1. Collect or obtain the monitoring variables during the smelting process of the Isa furnace and the current fault conditions. Each monitoring variable is used as a dimension in the feature space χ;

[0113] S4.2.2. Vectorize the collected data into X = {x 1 ',..., x' m}, where x i ' ∈ χ, and the corresponding fault condition to X is Y” = {y 1 ”,..., y″ m};

[0114] S4.2.3. Determine the kernel function, and find the maximum independent set X l according to the relevant algorithm, and the fault condition Y l corresponding to each element in X l ;

[0115] S4.2.4. Solve the system of equations in Equation (20) to obtain θ and b of the SLSSVM model;

[0116] S4.2.5. Construct an Isa furnace fault diagnosis model: where z is the new sampling result, z ∈ χ, and y(z) represents the result predicted by the fault diagnosis model.

[0117] S5. Verify the (KPCAL1 - SLSSVM) model constructed in S4;

[0118] S5.1. Verify the fault prediction of the Isa furnace lance;

[0119] S5.2. Verify the prediction of the Isa furnace lining erosion.

[0120] Advantages of the present invention:

[0121] The present invention proposes a fault monitoring technology combining Kernel Principal Component Analysis based on clustering feature samples (KPCA-L1) and Sparse Least Squares Support Vector Machine (SLSSVM). Feature samples are extracted through fuzzy c-means clustering, and KPCA-L1 effectively reduces the dimension and computational complexity of the kernel matrix. Combined with the sparse processing of SLSSVM, the number of support vectors is reduced, significantly improving the real-time performance and generalization ability of the monitoring model. This method demonstrates excellent performance in dealing with multi-variable non-linear dynamic problems, providing a new approach to solving the fault monitoring problem under the complex operating conditions of Isa furnaces, and laying a technical foundation for improving equipment operation efficiency and production stability. Description of the Drawings

[0122] Figure 1 is the flow chart of the present invention;

[0123] Figure 2 is the network architecture diagram of the present invention;

[0124] Figure 3 is the T of the present invention 2 Fault prediction diagram; among them, part (a) is the fault prediction diagram KPCAL1-T 2 Prediction diagram; part (b) is the fault prediction diagram KPCA-T 2 Prediction diagram;

[0125] Figure 4 is the SPE fault prediction diagram of the present invention; among them, part (a) is the fault prediction diagram KPCAL1-SPE prediction diagram; part (b) is the fault prediction diagram KPCA-SPE prediction diagram;

[0126] Figure 5 is the comparative analysis diagram of the accuracy of the Isa furnace lance fault prediction of the present invention;

[0127] Figure 6 is the refractory material state prediction diagram of the present invention. Detailed Implementation Modes

[0128] The present invention will be further described in detail below with reference to specific embodiments.

[0129] As Figure 1 and Figure 2 shown, a method for monitoring Isa furnace faults based on KPCAL1-SLSSVM includes the following steps:

[0130] S1. Collect data during the smelting process of the Isa furnace;

[0131] Specifically, the data collected during the smelting process of the Isa furnace is corrected to remove some obvious outlier data, and at the same time, whether each acquisition sensor is working properly is monitored;

[0132] The collected data includes: temperature data, pressure data, gas and fluid data, furnace lining erosion data, liquid and slag data;

[0133] The temperature data includes: hearth temperature and furnace lining temperature; the hearth temperature reflects the degree of thermal reaction in the smelting environment; the furnace lining temperature is used to judge the thermal stability and durability of the furnace lining;

[0134] The pressure data includes: negative pressure inside the furnace and flue gas pressure; the negative pressure inside the furnace is used to monitor the gas flow and airtightness inside the furnace; the flue gas pressure reflects whether the flue gas emission process is normal;

[0135] The gas and fluid data includes: oxygen blowing amount, steam flow rate, flue gas flow rate, oxygen content and SO in the flue gas 2 , CO gas concentration; the oxygen blowing amount directly affects the reaction intensity inside the furnace; the steam flow rate affects the cooling efficiency of the waste heat boiler; the flue gas flow rate reflects the gas release situation during the smelting process; the oxygen content judges the efficiency of the oxidation reaction; SO in the flue gas 2 , CO gas concentration is used to judge whether the chemical reaction is normal;

[0136] The calibration of the data includes: baseline calibration and dynamic calibration; the baseline calibration is to manually adjust the sensor measurement value according to experience by comparing with the data of known standard samples; the dynamic calibration is to manually remove abnormal jump points based on the historical trend of the monitored data;

[0137] The data rejection methods include: threshold rejection, statistical rejection and physical constraint rejection; the threshold rejection is to reject the sampling point value greater than the threshold; the statistical rejection uses the standard deviation rule to reject the data points exceeding 3 times the standard deviation; the physical constraint rejection is to reject in combination with the physical laws of the smelting process;

[0138] The monitoring of the data is the self-check of the sensor to detect whether there are breakpoints or a constant value in the output signal of the sensor;

[0139] The judgment of whether the sensor is normal includes: process specifications and historical data;

[0140] S2. Preprocess the data collected during the Isa furnace smelting process through the feature sample extraction kernel principal component analysis model (KPCA-L1); the steps are as follows:

[0141] S2.1. Construct a kernel principal component analysis model (KPCA-L1) to reduce the dimension of the data;

[0142] KPCA-L1 is a non-linear dimensionality reduction model proposed to further enhance the sparsity of the traditional KPCA method and simplify the dimensionality reduction calculation. Different from KPCA, KPCA-L1 introduces L1 regularization constraints in the kernel principal component analysis process, which can automatically select the most important sparse features for fault monitoring while ensuring the dimensionality reduction effect, reduce the computational complexity, and enhance the interpretability of the dimensionality reduction results. Its core idea is to use the kernel function to non-linearly map the input data from the original low-dimensional space to a high-dimensional space F. In the high-dimensional space, the data distribution is closer to linear, which is convenient for feature selection and dimensionality reduction. Subsequently, feature sparsity is achieved through L1 regularization constraints to complete the dimensionality reduction process.

[0143] Specifically as follows:

[0144] For the sample set X = {x k | k = 1, 2,..., M} in the input space, where x k ∈R N , where M represents the number of samples and N represents the original dimension of the sample feature space; the original space R maps x k to the high-dimensional space F through the non-linear mapping φ, and the corresponding mapping is φ(x i ) ∈ F. In the high-dimensional space F, the original data x i 's image in the mapping space F is: Assuming the mapped data is zero-mean Then the covariance matrix of the mapping function φ(x i ) can be expressed as Equation (1):

[0145]

[0146] To achieve sparse feature selection, L1 regularization constraints are introduced on the basis of KPCA, and the optimization objective function is:

[0147] min||w|| 1 , subject to w T Cw = λw T w;

[0148] In the formula, w represents the principal component weight vector that meets the sparsity requirements; λ represents the eigenvalue; C represents the covariance matrix in the high-dimensional mapping space, which is used to describe the distribution characteristics of the input samples in the high-dimensional space. Its core role is to provide the covariance information of the principal components for the dimensionality reduction step, determine the direction of feature projection, and the mapping function φ(x i ) maps the input samples from the original space to the high-dimensional space F, and C describes the distribution of all samples φ(x i ) in the high-dimensional space and calculates the covariance relationship between samples.

[0149] In traditional PCA, the eigenvalues λ, λ ≥ 0 and eigenvectors V ∈ F are obtained by solving the equation λV = CV, and then there is Equation (2):

[0150]

[0151] For λ ≠ 0, all eigenvectors v are obtained according to Mercer kernel theory and can be defined as shown in Equation (3):

[0152]

[0153] where α i is the weight coefficient of the mapping function φ(x i ) of the first sample data point x i after mapping. The weight coefficient is automatically generated through an optimization problem, and thus Equation (2) is expressed as Equation (4);

[0154]

[0155] where m represents the number of effective samples sparsely selected from the high-dimensional feature space; the number of features automatically selected through L1 regularization in the optimization process satisfies m ≤ M, where M is the number of samples. m is used for normalized weight calculation, that is, the number of features after sparse selection is used to adjust the elements in the covariance matrix and appears in the weight normalization factor to reduce the influence of unimportant features on the projection direction; x i is the first sample data point after mapping; x j is the second sample data point after mapping, x i， x j ∈ R N , x i ≠ x j ;

[0156] Define the kernel matrix K as an M × M kernel function matrix, and the elements in the matrix are expressed as:

[0157] k ij = φ(x i ) · φ(x j ) (5)

[0158] Therefore, K can be used to simplify Equation (4) to obtain MλKa = K 2 a, that is:

[0159] Mλa = Ka (6)

[0160] where a = [a 1 , a 2 , ···, a m T ​, by solving Equation (6), the eigenvalue λ and the eigenvector weights a of the kernel matrix can be obtained; the eigenvalues of K are arranged in descending order as λ 1 ≥λ 2 ≥···λ m , and the eigenvectors of K are arranged as v 1 , v 2 ,..., v m ;

[0161] For the eigenvector v of the prediction sample in the high-dimensional F space k The projection onto is Equation (7):

[0162]

[0163] In the formula, φ(x) represents the mapped data; represents the eigenvector projection of x i ;

[0164] When , it needs to be adjusted to Equation (8):

[0165]

[0166] Then the elements in the kernel matrix are solved using Equation (9):

[0167]

[0168] In the formula, k ij represents the element in the kernel matrix; k im represents the effective number of elements in the kernel matrix; k nj represents the index range of the elements in the kernel matrix; k nm represents the index range of the effective number of the kernel matrix; n represents the index range;

[0169] Based on the above principle, the processing procedure of KPCA-L1 is as follows:

[0170] The sample set X is represented as the input matrix A;

[0171]

[0172] From Equation (5), the kernel matrix K is calculated; to eliminate the influence of the sample mean, the kernel matrix is corrected by the centering method Equation (9) to obtain

[0173] The Jacobi iterative method is used to calculate The eigenvalues λ' 1 ,..., λ' n , that is The eigenvectors v' 1 ,..., v'n ;

[0174] The eigenvalues are sorted in descending order (by selection sort) to obtain λ 1 ′ >... > λ n ′ and the corresponding eigenvectors are adjusted to obtain v 1 ′,..., v′ n ; During the feature extraction process, to achieve sparse dimensionality reduction, the principal component weight vector w that meets the sparsity requirements is added with an L1 regularization constraint;

[0175] Through the projection of the kernel matrix on the extracted eigenvectors where a represents the kernel matrix eigenweight, a = (a 1 ,..., a t ), t represents the number of features after dimensionality reduction, t ≤ N, and the obtained projection Y is the data obtained after the sample is dimensionally reduced by KPCA;

[0176] In summary, kernel principal component analysis is to perform principal component analysis in the feature space. In the feature space, it has the same characteristics as PCA: for example, in the feature space, the various principal components are uncorrelated, and most of the energy is concentrated in the first few largest principal components; however, due to the non - linear mapping, the non - linear principal components in the original input space may not have a clear meaning; in terms of dimensionality reduction and feature extraction, compared with PCA, KPCA - L1 can extract more principal components; if the number of training samples M is greater than the dimensionality N of the samples, for PCA, at most n principal components can be obtained: while KPCA - L1 can obtain m - 1 non - linear principal components;

[0177] S2.2. Construct a kernel principal element analysis method based on feature sample extraction (SKPCA - L1) to improve the model performance;

[0178] Based on PCA, KPCA adds a process of feature sample selection, uses a sparse optimization method to dynamically select feature samples, and improves the performance of PCA;

[0179] KPCA expression: k ij = φ(x i )·φ(x j );

[0180] The dimensionality reduction process depends on eigenvalue decomposition: z i = w T φ(x i );

[0181] The KPCA expression dynamically selects feature samples before calculating K: k ij = φ(x i ) t φ(x j) Dynamically select x i , and optimize dimensionality reduction;

[0182] Performance improvements include: computational efficiency, sparsity, real-time performance, and dimensionality reduction effect;

[0183] Computational efficiency: KPCA dynamically selects feature samples during dimensionality reduction, reduces the dimension of the kernel matrix, and lowers the computational complexity;

[0184] Sparsity: L1 regularization makes the dimensionality reduction result sparse and improves the interpretability;

[0185] Real-time performance: Sample selection and sparse optimization are suitable for online learning scenarios and improve the real-time performance of the algorithm;

[0186] Dimensionality reduction effect: KPCA is more flexible than PCA in sample feature extraction, can select representative samples, and enhances the effectiveness of the dimensionality reduction result;

[0187] The construction steps are as follows:

[0188] S2.2.1. Feature sample extraction;

[0189] During the feature extraction process of KPCA-L1, sparse selection of feature samples is achieved through L1 regularization, making the dimensionality reduction result more sparse and interpretable; the extraction of feature samples is based on the optimization process of sparse weights, as follows:

[0190] Principle of feature sample extraction: The original sample dataset is mapped to the high-dimensional feature space F through φ(x i ), and the data after mapping is φ(x i ); in the high-dimensional feature space F, L sparse feature samples are selected from X to form the feature sample set X i = {x s ,..., x s1 ,..., x sL} feature sample set S, such that it can represent the entire data distribution; construct the KPCA expression to dynamically select feature samples before calculating K, and its elements are: k ij = φ(x i ) t φ(x j ), which captures the non-linear relationship between samples; each mapped sample φ(x i ) can be approximated by the weighted sum of feature samples: where a i = (a i1 ,... a iL ) t , represents the estimated value projected onto the optimized direction, a iis to make and φ i the coefficient vector with the minimum reconstruction error. and φ i The reconstruction error can be expressed as: The smaller the reconstruction error, the higher the approximation degree of the feature samples to the original data. To select the feature samples and ensure sparsity, L1 regularization constraint is introduced, and the optimization objective is: L1 regularization acts on a i so that most weights tend to 0, and only a few non-zero weights are retained, thus automatically selecting important feature samples;

[0191] The goal of feature sample extraction is to extract the feature sample set S from the sample set, and S satisfies the representativeness index. Define the representativeness index J s to measure the quality of the feature sample set S;

[0192] Based on the selected feature sample set S, the low-dimensional projection of each sample is represented as eigenvalue decomposition: z i = w T φ(x i );

[0193] Covariance matrix optimization: Based on KPCA, the kernel matrix K is introduced with sparse regularization constraint, and the final optimization objective is: min|w| 1 , subject to: w T Cw = λw T w. By optimizing w, the main direction of the feature samples can be obtained and dimensionality reduction can be achieved;

[0194] Define where the value range of J s is (0, 1]. The smaller the value, the stronger the approximation ability of the feature sample set S to the original data;

[0195] The optimization objective is transformed into: That is, given the feature sample L, select the feature sample set that can maximize the representativeness index;

[0196] In the initial state, the feature sample set S is an empty set, and samples are gradually added to it. In each iteration, calculate the reconstruction error δ i and the representativeness index J s , and select the sample x s that can minimize J s and add it to the feature sample set S, and update the feature sample set S and the reconstruction error. Termination condition: When the size of the feature sample set reaches the preset L, or the reconstruction error δ i converges, stop the iteration;

[0197] S2.2.2. Perform kernel principal component analysis on the feature samples;

[0198] S2.3. Perform kernel function mapping and sparse feature dimensionality reduction algorithm on the feature samples;

[0199] The traditional PCA algorithm improves the computational efficiency. However, in the process of using PCA for modeling, there are still deficiencies in the selection of the initial samples, and the construction from the global distribution of the samples is not considered. Therefore, aiming at the characteristics of the data sample distribution of the Isa furnace, this paper proposes a sparse optimization method based on kernel function mapping and L1 regularization. KPCA-L1 is a dimensionality reduction method based on kernel principal component analysis (KPCA) and L1 regularization, aiming to further enhance the sparsity and interpretability of the principal components by introducing L1 regularization to optimize the feature vector weights; the goal of KPCA-L1 is to retain the main linear characteristics of the feature space while achieving effective dimensionality reduction processing;

[0200] Given the original sample set X = {x k |k = 1, 2,..., M} To capture the non-linear relationship between samples, the kernel function is used to map the samples from the original space to the high-dimensional feature space F; its mapping form is: φ(x i ) = [φ 1 (x i ), φ 2 (x i ),..., φ k (x i )] T ; The kernel function k(x i , x j ) is defined as: k(x i , x j ) = φ(x i ) · φ(x j );

[0201] To ensure the centering of K, the kernel matrix is adjusted using Equation (9), and the objective is optimized through the L1 regularization method;

[0202] Eigenvalue decomposition, perform eigenvalue decomposition on the adjusted kernel matrix to obtain the eigenvalues λ' and the corresponding eigenvectors v'; select the first p eigenvectors with the largest eigenvalues as the principal component directions after dimensionality reduction;

[0203] Dimensionality reduction projection: For each sample x i , its dimensionality reduction result is: z i = w T φ(x i ); The output result of KPCA-L1 is the projection matrix after dimensionality reduction;

[0204] The specific description of the KPCA-L1 dimensionality reduction algorithm based on kernel function and sparse optimization is shown in Algorithm 1;

[0205] Algorithm 1: KPCA-L1 Dimensionality Reduction Algorithm Based on Kernel Function and Sparse Optimization

[0206]

[0207] S3. Use the T 2 statistic and the SPE statistic as evaluation methods for non-linear fault diagnosis. The evaluation index is to calculate the degree of deviation of the data from the KPCA-L1 model, and then determine whether a fault has occurred;

[0208] The deviation of the calculated data is automatically calculated through computer simulation;

[0209] The steps are as follows:

[0210] S3.1. Construct the expression of the T 2 statistic;

[0211] T 2 = [t 1 , …, t p′ Λ -1 [t 1 , …, t p′ T (11)

[0212] In the formula: Λ -1 is a diagonal matrix, representing the inverse of the diagonal matrix composed of the eigenvalues corresponding to the first p' principal components;

[0213] The confidence limit expression of the T 2 statistic satisfies the F-distribution of Equation (12);

[0214]

[0215] In the formula: N' represents the number of samples in the set S, P′ represents the number of principal components; α represents the projection;

[0216] S3.2. Construct the expression of the squared prediction error (SPE):

[0217]

[0218] In the formula: when when j ≠ k The confidence limit of the SPE statistic satisfies an approximate distribution of, where g represents the weight parameter of the importance of SPE, h is the degree of freedom of the distribution, represents the chi-square distribution with degree of freedom h, t​j Denote x j The mapping function to the KPCA-L1 space, The t-th x k The eigenvector of, The t-th x j The eigenvector;

[0219] S3.3. Analyze through simulation;

[0220] For the preliminary fault identification, actual data from a smelter is used for simulation analysis and research to verify the effectiveness of the algorithm. According to decades of production conditions and expert experience, 10 main variables are selected for KPCA research on the furnace condition. These variables include the furnace temperature, negative pressure, oxygen blowing volume, water level of the waste heat boiler, steam flow rate, temperature, flue gas negative pressure, flue gas flow rate, oxygen content of the flue gas, and CO content. Multiple-point measurements are required to prevent flue gas stratification. Taking the Isa furnace in a smelter as an example, a KPCA-L1 model is established. First, 960 sampling data under normal operating conditions in the steady state are taken, including: furnace temperature, negative pressure, oxygen blowing volume, water level of the waste heat boiler, steam flow rate, temperature, flue gas negative pressure, flue gas flow rate, oxygen content of the flue gas, and CO content; each sampling includes the complete measurement values of the above 10 variables, and a total of 960 groups of data are sampled to establish the KPCA-L1 model. In this way, the reliability of the model can be ensured. After multiple value-taking experiments, the kernel function of KPCA-L1 selects the radial basis function, and when the parameter σ of the kernel function is 0.09, KPCA-L1 can achieve better dimensionality reduction and classification effects. The following takes the fault state as an example for analysis. Under the monitoring of abnormal states, 960 groups of test data are obtained for on-line process monitoring (the sampling time is 5 minutes).

[0221] Figure 3 and Figure 4 are the statistical quantities T 2 and the KPCA-L1 prediction diagrams of SPE. Figure 3 Part (a) in is the fault prediction diagram KPCAL1-T 2 prediction diagram, and part (b) is the fault prediction diagram KPCA-T 2 prediction diagram; Figure 4 Part (a) in is the fault prediction diagram KPCAL1-T 2 prediction diagram, and part (b) is the fault prediction diagram KPCA-T 2 prediction diagram; The training samples used are the feature samples extracted from the whole samples, and the feature samples are only 90 of these 960 samples. It can be seen from the figure that the fault diagnosis effects of KPCA-L1 and KPCA based on the whole samples are almost the same, but the former uses small samples to establish the principal component model. If it is used for real-time on-line prediction, only these small samples need to participate in the operation. Therefore, the calculation amount of the former is greatly reduced.

[0222] From the results, it can be seen that the KPCA-L1 algorithm can not only effectively judge the faults in the Isa furnace smelting, but also has good data dimensionality reduction ability. Therefore, it provides a basic guarantee for the subsequent specific classification of faults.

[0223] S4. Establish a sparse least squares support vector diagnostic model (SLSSVM), and input the faults identified in S3 into the sparse least squares support vector diagnostic model for analysis to complete the identification and classification of faults; specifically as follows:

[0224] S4.1. Establish a sparse least squares support vector diagnostic model (SLSSVM);

[0225] The support vector machine is a typical representative of statistical machine learning theory and has good generalization ability. In the metallurgical industrial process, it is widely applied to various fault monitoring environments. However, SVM needs to solve the quadratic programming problem under inequality constraint conditions, which increases the difficulty and complexity of the solution. To solve this problem, LSSVM converts the inequality constraint conditions in SVM into equality constraint conditions for solution, reducing the computational complexity. But at the same time, it also brings new problems, that is, LSSVM requires all samples to participate in training, losing the advantage that SVM only needs a limited number of samples to participate in training. For the real-time requirement of Isa furnace fault monitoring, LSSVM will inevitably lead to a reduction in timeliness. Therefore, the present invention simplifies LSSVM using the sparse LSSVM algorithm (SLSSVM) and proposes a sparse least squares support vector diagnostic model for Isa furnace fault identification.

[0226] The least squares support vector machine is a model based on the structural risk minimization theory. Let X' = [x' 1 ,..., x' N' represent the training samples, which in the Isa furnace represents a set composed of N' data samples, where each sampling includes the data collected during the Isa furnace smelting process; Y' = [y' 1 ,..., y' N' represents the condition of the Isa furnace for each sampling. The formal description of LSSVM is as shown in Equation (14):

[0227]

[0228] In the formula: w′ is the normal vector of the (LSSVM) classification model, b represents the offset, e k' is the slack variable; γ represents the balance sparsity between the structural risk and the empirical risk; x k' represents the number of principal component mappings;

[0229] Using the Lagrange multiplier method to solve Equation (14), the following Lagrangian function can be obtained:

[0230]

[0231] where \(L(w', b, e k' , \alpha k' ) is the Lagrangian function; \(\alpha k' is the Lagrange multiplier; then, by taking the derivatives of the variables in Equation (15) respectively, we can obtain:

[0232]

[0233] Let Y' = [y' 1 ,..., y' N' , 1 v' = [1,..., 1] represents a vector composed of \(v'\) 1s; \(\alpha\) represents the vector composed of Lagrange multipliers, \(\alpha = [\alpha 1 ,..., \alpha N' ; combining with the KKT conditions of the optimization theory, Equation (16) can be expressed in matrix form:

[0234]

[0235] where: \(E\) represents the identity matrix, \(\Omega = Z T Z\), represents the matrix of kernel function values with class information, and the elements in \(\Omega\) are defined as:

[0236]

[0237] where \(K(x i , x j ) is the kernel function. In the kernel method, the commonly used kernel functions have the following forms:

[0238] Gaussian kernel function, polynomial kernel function, wavelet kernel function, and perceptron kernel function:

[0239] Equation (17) can be used to solve for \(\alpha k' and \(b\), and then construct the final diagnostic function \(y(x)\), as shown in Equation (19) specifically:

[0240]

[0241] where \(y(x)\) represents the classification output of the model for the input \(x\), and the classification result is +1 or -1; \(sign\) represents the sign function, which returns the sign of the input value; \(\alpha k' represents the Lagrange multiplier, obtained through optimization, indicating the weight of the sample; \(y k' represents the label of the \(k\)-th sample, taking values of +1 or -1; \(K(x, x k ) is the kernel function, representing the kernel between \(X\) and the \(k\)-th sample \(x kSimilarity; b represents the bias parameter, which is solved by the optimization problem;

[0242] As can be seen from Equations (17) and (8), LSSVM requires all sampled data to participate in training during the training process. From Equation (15), it can be seen that w′ is a linear combination of input vectors in the feature space. If the maximum linearly independent group of input vectors in the feature space can be obtained, then an LSSVM with only part of the sampled data participating in training, that is, a sparse LSSVM (SLSSVM), can be obtained. In the specific sparsification process, the method used in the present invention is as follows. The specific SLSSVM model is expressed as:

[0243]

[0244] In the formula: X l is the sample set with the maximum irrelevance; θ = [θ 1 , θ 1 ,..., θ 1 T ; l is the number of elements in X l ; J p′ (θ) represents the loss function, and the goal is to minimize this function to optimize the model; θ represents the weight vector, which is used to represent the direction of the classification hyperplane in the feature space; similar to solving LSSVM, according to the Lagrange multiplier method, Equation (20) is solved, and the resulting system of partial derivative equations is converted into an equivalent matrix expression, and then Equation (21) is obtained;

[0245]

[0246] In summary, the solution of SLSSVM is completed.

[0247] S4.2. Construct an Isa furnace diagnosis model based on SLSSVM; the steps are as follows:

[0248] S4.2.1. Collect or obtain the monitoring variables during the Isa furnace smelting process and the current fault conditions. Each monitoring variable is used as a dimension in the feature space χ;

[0249] S4.2.2. Vectorize the collected data into X = {x 1 ',..., x' m}, where x i ' ∈ χ, and the corresponding fault condition to X is Y” = {y 1 ”,..., y″ mn};

[0250] S4.2.3. Determine the kernel function, and find the maximum independent group X l according to the relevant algorithm, and the fault condition Y corresponding to each element in X l ​​l ;

[0251] S4.2.4. Solve the system of equations in Equation (20) to obtain θ and b of the SLSSVM model;

[0252] S4.2.5. Construct an Isa furnace fault diagnosis model: where z is the new sampling result, z ∈ χ, and y(z) represents the result predicted by the fault diagnosis model.

[0253] S5. Verify the (KPCAL1 - SLSSVM) model constructed in S4;

[0254] The Isa smelting process is as follows: The furnace charge is fed from the top of the furnace, and air or oxygen - enriched air is blown into the molten bath through an immersion lance set at the center of the furnace top. The injection pressure is 0.1 MPa, and the molten bath temperature is controlled at (1200 ± 40) °C. The furnace body adopts a vertical cylindrical structure with a refractory lining. The lance is inserted below the molten slag layer of the molten bath to send air or oxygen - enriched air to the liquid layer of the molten bath, forming a strongly agitated molten bath. After the furnace charge is fed from the top of the furnace, it directly falls into the molten bath and quickly undergoes a chemical reaction with the blown - in oxygen under the agitated state, completing melting and generating slag and copper.

[0255] The Isa furnace body is a closed - type structure, and the internal metallurgical chemical reaction proceeds efficiently under closed conditions. To ensure the stability and safety of the smelting process, key process parameter data inside the furnace are collected in real - time, the state of the molten bath is monitored, the furnace condition changes are judged based on the detected data, and whether there are faults is identified, so as to ensure the normal operation of the smelting process.

[0256] S5.1. Verify the prediction of the Isa furnace lance fault;

[0257] The present invention proposes a spray gun fault diagnosis method based on kernel function and sparse optimization, aiming to solve the problems of low diagnosis efficiency and insufficient accuracy of existing monitoring methods under complex working conditions. The method includes the following steps: First, collect multi-dimensional characteristic variables during the operation of the spray gun in real time, including data such as furnace temperature, pressure, oxygen content, steam flow, etc., and preprocess the original data, including removing outliers, abnormal values and normalizing; Second, use the kernel function method to map the data to a high-dimensional feature space, and perform sparse feature extraction and dimensionality reduction analysis based on the KPCA-L1 algorithm. By introducing L1 regularization constraints, the selection and dimensionality reduction of characteristic variables are realized, and the sparsity and interpretability of the model are improved; Then, construct an optimal LSSVM diagnosis model based on the dimensionality-reduced data, optimize the kernel parameters and relaxation variables to achieve efficient identification and classification of spray gun fault modes; Finally, by dynamically updating the model parameters and feature contribution rates, combine the diagnosis results to generate specific fault categories and possible causes, and present the diagnosis information through a visualization tool, so as to realize real-time monitoring and fault prediction of the spray gun operation state. The method of the present invention significantly improves the diagnosis efficiency, real-time performance and fault classification accuracy, is applicable to the spray gun operation state monitoring under complex working conditions, and has wide industrial application value. Therefore, the SPCAL1-SLSSVM model proposed by the present invention can be used to predict the faults of the Isa furnace spray gun.

[0258] During the prediction process, in order to reflect the fault conditions of the spray gun, in the experiment process, for each type of fault, including: the burning damage of the spray gun end, the wear of the spray gun end pipe wall and the swirling flame burning damage, four grades are divided, namely <normal, slightly damaged, potential fault, fault>, constituting 3 directions and 12 small states. For each state, 15 groups of data are taken, and the SLSSVM is used to train 180 groups of training samples obtained after being processed by the KPCA-L1 algorithm. The prediction models are constructed by using Gaussian kernel function, polynomial kernel function, wavelet kernel function and perceptron kernel function respectively, and the parameters of each kernel function are adjusted by using the iterative detection method and the ten-fold cross-validation method. When testing, 10 groups of samples are set for each state, and a total of 120 groups of samples participate in the prediction. For comparison, relevant comparative experiments are also carried out based on KPCA-SVM and KPCA-LSSVM. Table 1 shows the prediction results under different kernel functions. Figure 5 It is the experimental results of multiple methods. Among them, each type of fault contains the above four grades of subtypes, so each type of fault is composed of 60 groups of training data and 40 groups of test data.

[0259] Table 1 Experimental results of the prediction accuracy of the Isa furnace spray gun fault based on KPCAL1--SLSSVM Table 1 shows that the selection of kernel function has a certain influence on the fault prediction results. Among them, the Gaussian kernel function is more effective than other kernel functions, and the average precision reaches 85.4%. The wavelet kernel function ranks second. The perceptron kernel function and the polynomial kernel function have the same effect in the fault detection of the Isa furnace lance. Therefore, the KPCAL1--SLSSVM model based on the Gaussian kernel will be used for prediction in actual detection.

[0260] Figure 5 It is a comparative analysis chart for predicting the lance fault based on KPCAL1--SLSSVM, KPCA-LSSVM, and KPCA-SVM. The Gaussian kernel function is used for all kernel functions. The experimental results show that the method based on KPCAL1--SLSSVM has a significant improvement in accuracy compared with other methods, with an increase of 15.4% compared with KPCA-LSSVM and an increase of 20.8% compared with KPCA-SVM.

[0261] S5.2. Verify the prediction of the Isa furnace lining erosion;

[0262] Isa smelting is a submerged oxygen-enriched top-blown bath smelting technology. The Isa furnace is vertically cylindrical in shape and lined with refractory materials. During the actual smelting process, due to strong chemical reactions, the furnace lining is eroded, resulting in a shortened service life. The lining erosion under high-intensity smelting is a very complex theoretical and practical problem. There are many factors affecting the erosion of the Isa furnace lining, and these factors interact with each other. Through practice, it is found that the core of predicting the furnace lining erosion is the prediction of refractory materials.

[0263] In terms of the chemical erosion of the refractory materials of the furnace lining, the main mechanism of chemical erosion of refractory materials during the Isa furnace smelting process is that the slag diffused into the bricks reacts with the periclase in the bricks to form olivine phase, forming a metamorphic layer with different structures and properties from the original magnesia-chrome bricks. In terms of the agitation and erosion of the melt, the greater the agitation intensity of the melt, the more severe the erosion of the furnace wall, accelerating the mechanical erosion of the refractory materials. The lining erosion of the PS converter is a typical example. The thermal stability in the Isa furnace also has an important impact on the service life of refractory materials. During the use of refractory materials, due to the drastic temperature fluctuations, the cracks parallel to the working surface are generated in the metamorphic layer formed after being eroded by the slag under the action of thermal stress, resulting in the cracking and spalling of the metamorphic layer.

[0264] Therefore, aiming at the possible conditions of the refractory materials in the Isa furnace, they are divided into four prediction directions: the penetration depth of the eroded brick layer, the corrosion area, the cracking area, and the spalling area. And each direction is similar to the prediction of the spray gun and is divided into four grades <normal, slightly damaged, moderately damaged, severely damaged>. 10 groups of data are collected for each state, forming 160 groups of data, and then the KPCAL1-SLSSVM algorithm is used to solve. The kernel functions of KPCAL1 and SLSSVM both adopt the Gaussian kernel function, and the determination of the kernel function parameters is obtained by iterative detection and ten-fold cross-validation. 10 groups of samples are also set for each state for the test samples, and a total of 160 groups of samples participate in the experiment. The experimental results are as Figure 6 shown.

[0265] Figure 6 Figure

[0265] is a comparative analysis chart for predicting refractory materials based on KPCAL1-SLSSVM and KPCA-SVM. The ordinate represents the prediction accuracy, and the abscissa represents different fault categories, where 1 to 4 represent the penetration depth level, 5 to 8 represent the corrosion area level, 9 to 12 represent the cracking area level, and 13 to 16 represent the cracking area level. The experimental results show that the method based on KPCAL1-SLSSVM has a higher prediction accuracy.

[0266] The present invention first conducts an in-depth study on the problem of Isa furnace fault prediction, preprocesses the sampled data using the KPCA algorithm based on L1 regularization constraint, and then uses T 2 and SPE statistics to preliminarily identify faults. Then, the KPCAL1-SLSSVM algorithm is used to conduct prediction experiments on the spray gun and lining states of the Isa furnace. The experimental results show that this method has good prediction accuracy, fully utilizes the advantages of the KPCAL1 and SLSSVM models, can quickly reflect the changes and faults in the entire production process, can work online in real time, and is suitable for popularization and application in similar industrial processes.

Claims

1. A KPCAL1-SLSSVM-based Isa furnace fault monitoring method, characterized in that: The following steps are involved: S1. Collect data during the ISA furnace smelting process; The collected data include: temperature data, pressure data, gas and fluid data, lining erosion data, liquid and slag data; S2, preprocessing the data collected during the ISA furnace smelting process through feature sample extraction and principal component analysis model; S3. Use T 2 Statistics and SPE statistics are used as evaluation methods for nonlinear fault diagnosis. The evaluation index is the degree to which the calculated data deviates from the characteristic sample extraction kernel principal component analysis model, and then determines whether a fault occurs; S4, establishing a sparse least squares support vector diagnosis model, and inputting the faults identified in S3 into the sparse least squares support vector diagnosis model for analysis to complete fault identification and classification; S5. Verify the model constructed in S4.

2. The Isa furnace fault monitoring method based on KPCAL1-SLSSVM according to claim 1 is characterized in that: The steps of preprocessing the data collected during the ISA furnace smelting process by using the feature sample extraction and principal component analysis model are as follows: S2.1, construct a kernel principal component analysis model to reduce the dimension of the data; The kernel principal component analysis model is obtained by introducing the L1 regularized kernel constrained principal component analysis model, wherein the expression of the kernel principal component analysis model is as follows: k ij =φ(x i )·φ(x j ) In the formula, x i represents the first sample data point after mapping; x j Represents the second sample data point after mapping, x i， x j ∈R N , x i ≠x j ; N represents the original dimension of the sample feature space; φ represents nonlinear mapping; The optimization objective function expression of L1 regularization is as follows: min||w||1,subjectto w T Cw=λw T w; Where w represents the principal component weight vector that meets the sparsity requirement; λ represents the eigenvalue; C represents the covariance matrix in the high-dimensional mapping space; S2.

2. Construct a kernel principal element analysis method based on feature sample extraction to improve model performance; the construction steps are as follows: S2.2.1, feature sample extraction; The goal of the feature sample extraction is to extract a feature sample set S from a sample set; S2.2.2, perform kernel function principal component analysis on feature samples; S2.

3. Perform kernel function mapping and sparse feature dimensionality reduction algorithm on feature samples.

3. The Isa furnace fault monitoring method based on KPCAL1-SLSSVM according to claim 1 is characterized in that: The use of T 2 Statistics and SPE statistics are used as evaluation methods for nonlinear fault diagnosis. The evaluation index is the degree to which the calculated data deviates from the characteristic sample extraction kernel principal component analysis model. The steps to determine whether a fault occurs are as follows: S3.

1. Construction of T 2 Expressions for statistics; S3.2, construct an expression for the squared prediction error; S3.

3. Analysis through simulation.

4. The Isa furnace fault monitoring method based on KPCAL1-SLSSVM according to claim 1 is characterized in that: The steps of establishing a sparse least squares support vector diagnosis model and inputting the fault identified in S3 into the sparse least squares support vector diagnosis model for analysis to complete the identification and classification of the fault are as follows: S4.

1. Establish a sparse least squares support vector diagnosis model; the expression is as follows: Where: X l is the set of samples with maximum irrelevance; l is X l The number of elements in J p′ (θ) represents the loss function, the goal is to minimize this function to optimize the model; θ represents the weight vector, which is used to represent the classification hyperplane direction in the feature space, θ = [θ1, θ1, ..., θ1] T ; γ represents the balance between structural risk and empirical risk; N' represents the set of N' data samples of Isha furnace in the training sample; x k' represents the number of main element mappings; b represents the offset; e k' is the slack variable; S4.

2. Construct an Isa furnace diagnostic model based on the sparse least squares support vector diagnostic model.

5. The Isa furnace fault monitoring method based on KPCAL1-SLSSVM according to claim 1 is characterized in that: The steps for verifying the model constructed by S4 are as follows: S5.

1. Verify the prediction of ISA furnace spray gun failure; S5.

2. Verify the prediction of ISA furnace lining corrosion.

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